A car journey of 380 km lasts 4 hours. Part of this is on a motorway at an average speed of 110kmh^-1, the rest on country roads at an average speed of 70kmh^-1.
(i) Write this information as pair of simultaneous equations.
(ii) Solve you equations to find how many kilometres of the journey is spent on each type of road.

So, I know what the answers are but I can't figure out how to get to it myself. Please will you help by showing me how?

Question

A car journey of 380 km lasts 4 hours. Part of this is on a motorway at an average speed of 110kmh^-1, the rest on country roads at an average speed of 70kmh^-1.
(i) Write this information as  pair of simultaneous equations.
(ii) Solve you equations to find how many kilometres of the journey is spent on each type of road.

So, I know what the answers are but I can't figure out how to get to it myself. Please will you help by showing me how?

welshfella · Answer

use the relation v = d/t
v= speed , d = distance travel on a motorway and t = time taken on the motorway

so for motorway travel we have

110 = d/t

and for the country roads

70 = (380 - d) / (4  - t)

welshfella · Answer

so there are your 2 equations

welshfella · Answer

writing the equation without fractions we get

d = 110t

380 - d = 70(4 - t)

to solve for t 
substitute d = 110t in the second equation

380 - 110t = 280 - 70t
380 - 280 =  110t - 70t

can you continue with this?

welshfella · Answer

oh  they want number of kilometers on each type of road 
I should have solved for d

no matter when we find t we can then plug in the values to find the distances

welshfella · Answer

fo you follow it OK so far?

welshfella · Answer

are you there?

anonymous · Answer

Yes, I am just a bit confused since those are not the answers my book got? I will give those too you now...

anonymous · Answer

t(subscript 1) + t(subscript 2) =4;
110t(subscript 1) + 70t(subscript 2) = 380

Sorry I cant type the subscript numbers on my computer.

anonymous · Answer

That is what my textbook has said are the answers to the first question.

welshfella · Answer

yes  thats basically the same as i have bu they have called the two times t1 and t2

whereas ive called them t and 4 - t  because   total time was 4 hours

welshfella · Answer

if you solve for t you;ll find t = time for motoirway journey = 2.5 hours and so time foe road journey = 4-2.5 = 1.5

and distance for motorway = 110 * 2.5 = 275km
and for raoad = 70 8 1.5 = 105 km

welshfella · Answer

t1  + t1 = 4
110 t1 + 70 t2 = 380

is what your book has said

welshfella · Answer

do you want me to show you how to solve this?

welshfella · Answer

there is often a few different ways to solve problems like this.

anonymous · Answer

Oh ok. I think I understand now- thank you very much!

welshfella · Answer

oh that should be t1 + t2 = 4

welshfella · Answer

yw

welshfella · Answer

t1 being time for motorway and t2 time for roads

anonymous · Answer

Ok. You have helped me a lot!

welshfella · Answer

yw